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Tuesday, May 08, 2007

Millikan Oil Drops

As you might know, I am interested in the possibility to experimentally test quantum gravity. The big obstacle on the way to doing so is that the effects are extremely small, because gravity is so weak. It might not seem all that weak to you, gravity being what holds you down to your chair right now, but the only reason why we observe it at all is that gravity - unlike all of the other interactions - can not be neutralized, and so it adds up. But if you think about it, if you pin a magnet to your fridge, that tiny magnet's force is sufficient to act against the gravitational pull of the whole earth.

If one estimates as an example the ratio between the electric and the gravitational force between two electrons one finds [1]

Where mpl is the so-called Planck-mass and related to the gravitational constant as 1/mpl2 = G. That is, the gravitational interaction in this case is by roughly 43 orders of magnitude smaller than the electric one. The reason for this is that the mass-scale associated with gravity, the Planck-mass, is much much larger than the typical particle masses. Nobody knows why that is, this is also called the 'Hierarchy problem'. On the other hand, macroscopically seen the Planck-mass isn't a large mass at all. In fact, it is a scale that is perfectly handy for experiments. In grams, the Planck-mass is roughly 22 micrograms.

Last year, I came across a paper by Dr. Raymond Chiao who proposes an experiment to exploit this fact

Naturally, I was very interested and looked into the topic. Since there were many details I didn't understand, I have been in email contact with the author for some while. Three months ago, there was a newer, and more extended version on the arxiv: gr-qc/0702100, which caused me to again contact Dr. Chiao. In the following I would like to share my concerns about the effect explained in these works.

The proposal is to use objects of about Planck-mass that only carry a total electric charge of order one. For these objects, the electric and gravitational force would then be of roughly the same strength. The concrete scenario which Chiao describes uses something called 'Millikan Oil Drops'. I admit that I don't understand all the features of these drops, but essentially these are cooled and super-fluid helium drops coated with electrons. Their superconductivity is claimed to be an important part of the experimental setup.

These drops, so the claim, would be strongly coupled to gravitational radiation, and could amplify it such that it becomes detectable [2]. Essentially you can envision a pair of drops acting like an antenna. Excited through a periodic electromagnetic field, they would emit both electromagnetic and gravitational radiation. It is argued that gravitational radiation has to be as strong as the electric radiation, because the droplets are designed such that they are equally strong subject to both forces: "This is a strong hint that mesoscopic-scale quantum effects can lead to non-negligible couplings between gravity and electromagnetism that can be observed in the laboratory."

The first obvious objection that springs into my mind is, yes, both forces act equally. But equally weak. There is no way the process of simply cooling matter can affect the gravitational force, unless one introduces some kind of modification of gravity. But Chiao claims this is an effect of purely classical general relativity, and there is no modification necessary. I was looking for a derivation of the gravitational wave emission. There is none, in neither work. All that one can find is the electromagnetic case, and then the repeated argument that the gravitational case is identical. In such a way, Chiao derives the drops are reflecting gravitational waves: "Hence it follows that nearly perfect reflection of gravity waves should occur from a superconductor at temperatures well below its transition temperature."

This argument can very easily be defeated. The electric charge of the drop is confined to the surface (they are 'coated'). The mass of the objects is equally distributed throughout the drop. Thus, the source terms for both, electromagnetic and gravitational field are not equal. The argument that both can be treated by applying a symmetry principle just does not apply. Though in a linear approximation of gravity both are essentially described by a wave-equation, both have different initial values. The paper says: "From the Maxwell-like equations [...], and the boundary conditions that follow from them, it follows that there should exist an analogous reflection of a gravitational plane wave from a planar vacuum-superconductor [...]". The boundary conditions hardly ever follow from the equations.

I also totally don't understand why one could possibly expect superconductivity to enhance classical gravitational effects. The argument relies on a postulated symmetry between gravitational and electromagnetic behavior. Even if one believes it, this symmetry would be based on the low temperature and the amazing properties of the droplets. Yet, the gravitational field of the droplets doesn't change with the temperature. How then can such an experiment possibly change the behavior for gravitational waves? I do understand that the electromagnetic properties change, but I find it extremely implausible to conclude from that that the gravitational field is also affected [3].

Since the effect can not be caused by the electric properties of the electrons, it had to be caused by their motion. It could then only be the masses of the electrons that cause the gravitational radiation to be strong. But this is more than implausible. The whole setup takes place in the linear regime of gravity. The total mass of all of the electrons is many orders of magnitude lower than the total mass of the droplets. A contribution to the gravitational field that is several orders of magnitude smaller can in the linear regime not result in a radiation that is several orders of magnitude larger (than that of the object without the electrons).

There has been some experimental evidence that superconducting materials might display unusual gravitational effects. I am somewhat sceptical about that, but it might be possible. Who knows? That is, the proposed experiment might be worthwhile to do. However, whether or not there is such an effect, I have very strong doubts about the explanation offered in Dr. Chiao's papers.

Aside: I would have liked to share here part of my email communication with Dr. Chiao to make sure I did not misinterpret his explanations, but he didn't agree on that [4].

Footnote 1: The speed of light and Planck's constant are equal to one, so are maybe occurring factors of some pi or 137 or so.

Footnote 2: One should note here that gravitational radiation has never been directly detected. Indirect detection through radiative loss in binary systems was awarded with the Nobel Prize in 1993.Footnote 3: Strictly spoken, the gravitational field of course is affected if the electromagnetic field changes since the electromagnetic field strength also is a source to the field equations. However, compared to the mass of the objects this is a negligible effect. It neither affect the conclusion, nor is it claimed by Chiao to be responsible for the effect.

25 comments:

These claimes sound bogus to me. The analogy between electro-magnetism and gravity (i.e. the similarity between Coulomb's law and Newton's law) hold only on the level of static sources. When it comes to radiation there is the significant difference that dipole radiation --- the dominant part in the electromagnetic case --- is not possible in the gravitational case because of momentum and angular momentum conservation.

Thus while the power radiated by an electric dipole is roughly d^2p/dt^2 where p is the dipole moment, the power of gravitational radiation is (up to indices and numbers) d^3 I/dt^3 where I is the reduced second moment of mass distribution. This (and especially its third time derivative) should be increadibly small form microscopic drops of any earthly material. And it goes like M^2 L^4 thus it's not a good idea to look at _small_ things.

Indeed, I agree when it comes to the far field (when one is concerned with the field strength itself, it's more the density that matters.) One way or the other, if one has a small 'drop' of whatever, with whatever charge, whatever temperature (!), superconducting or not, that doesn't suddenly make it a stronger emitter of gravitational waves.

Yes, and of course, it's a different spin (that also being responsible for gravitational force being attractive among like charges, whereas a vector interaction is repulsive.)

So the paper is bunk, but there could be a really cool experiment in there:

With the oil drop experiments the essential idea is to precisely balance a very lightly charged particle between two electrostatic plates. Now the question is what happens when one keeps the eletrostatic gradient the same, but changes the gauge potential. Shouldn't large changes in the gauge, cause changes in the stress-energy, thereby changing the gravitational potential. Admittedly the effect would be very small.

Or how about gravitational deflection of the droplet by a passing photon, one could shine a very bright high frequency laser near but not at the droplet and try to detect changes in its balance position.

If you are really clever you could set up the electrostatic field so that it is not linear, thus changes in gravitational potential could be seen in changes of position. One could probably achieve this using a laser forceps technology to balance microsopic particles.

Actually the slickest experiment would be to use alternating ato-second beams: one that provides an electrodynamic counter force and the other that provides a doppler velocity measurment, from which one can estimate gravitational acceleration while the electrodynamic balance laser is off.

Radio waves and and gamma rays are different ways at looking at frequency?

If one was to think of the uncertainty and the idea of high energy photons, what rules of kaluza and klein would have said that we can now move to a fifth dimensional perspective here? That a method of grvaity and light had been joined?

So you would look at the sun and know that in gamma ray it would reveal what about the nature of it's actions. We would se this different then we would in radio waves?

your comment just arrived while I was in the colloq by Raman Sundrum about gravity in 5 dimensions... I am afraid though I don't understand your question. The only difference between radio waves and gamma rays are their frequencies. If you add a fifth dimension, they could in principle also travel into this additional direction. Just that it takes very much energy to do so, the smaller the dimensions, the more energy it takes. That's why it might be that the additional dimensions have remained unobserved so far. Energies that we typically have for gamma rays or radio waves are not sufficient for that.

Q9's article about photosynthesis posted in haloscan on my site somehow seems to make sense when ones think about new comnputerized systems, and endocrinology being mimic'ed as used in our biological system.

It seems Newton was not the only one that saw potential in color/sound music organs it's relation to what gravity might be pecieved as?

in my post above I linked to the very same article. As I have stated there, I am sceptical about the results, but I do not think it is impossible. If confirmed however, I would guess this is not an effect of standard gravity. This is what confuses my about Chiao's paper: that he claims one could explain such with standard GR, which is most definitely just not the case (even more confusing since it would be much more exciting if it weren't).

The reason why I am sceptical about this is that I imagine it very difficult to precisely measure an attractive force in the presence of such strong electric fields acting on the samples, and everything rotating etc 'a ring of superconducting material rotating up to 6 500 times a minute' sounds pretty challenging to me. I would guess (being a bit pessimistic here) that it is a systematic error in the setup. But then, I haven't looked into the details, and I don't plan on doing so. That's just my opinion since you asked for it.

Haha! I'm 4 * 10^9 Plank masses, approximately. I walk across the carpet and pick up a electric static charge. Human capacitance is supposedly 100-200 pF, and since I can make a spark, I must be getting a few thousand volts. So somewhere in walking across the carpet, I cross a charge of 4 * 10^9 electron charges, at which point I'm a huge agglomeration of Prof. Chiao's "Millikan drops". I'm sure I have a greater quadrupole moment than Prof. Chiao's drops. I suppose I emit gravitational radiation, and that radiation, emitted by 6 billion people like me is what is keeping LIGO from being successful - too much noise?

Does it make any difference if gravity is a lot stronger at distances comparable to the oil drop size?

It should not affect the far field. The thing with short distance modifications of gravity is that in the macroscopic limit they reduce to the standard scenario. If an object of that size were a strong emitter of gravitational radiation, we'd already have noticed. Molecules e.g. would loose energy all the time through gravitational radiation.

Also, in this case the analogy between the gravitational and electromagnetic case would hold even less.

If I understand it right, the PM is the smallest possible mass for a black hole, right?

Nobody really knows what happens at these scales, but this is what most believe, yes. If a black hole has about Planck mass, then the curvature at the horizon reaches the Planckian regime and is potentially subject to quantum effects.

btw: why is planck length radius so important? the cross dection (Durchmesser) 2r, could still be large enough to cover the Planck length. (of a micro black hole)

Yeah, well, some factors of order 2 Pi/d+1 or so come and go into this definition (that is supposed to say some define the Planck mass with additional geometric prefactors, some don't). The important thing is the order of magnitude. That is to say most of the expectations might be off by a factor of order ten or so. Say, the minimum black hole mass (if existent) might not be 22 micrograms, but maybe 4 or 100. Best,

22 mcg Helium II microdrops bearing one extra electron each are experimentally silly. With near-zero heat of vaporization and 100 Pa vapor pressure at 1.23 K, they will not persist - certainly not if you look at them and thereby introduce energy. With a refractive index ~1.02 there won't be much to see.

A black hole is an object so massive that even light cannot escape from it. This requires the idea of a "gravitational mass" for a photon, which then allows the calculation of an escape energy for an object of that mass. When the escape energy is equal to the photon energy, the implication is that the object is a "black hole."

the only thing that comes into my mind is 'If I didn't see farther than others, it's because giants were standing on my shoulders' (and that wasn't even my idea, I read it somewhere, even worse, I forgot who said it). Business here at PI is so busy it keeps me jumping on my toes, and I am not getting anywhere.

Today however the weather is pretty nice and sunny. My weather ticker says, it's actually better than in Santa Barbara (well, the winter was definitely long enough). Anyhow, I miss the beach. The only insight that I've had today was that I should have payed my credit card bill before attempting to go grocery shopping. Gnagnagna.

The sentence When the escape energy is equal to the photon energy, the implication is that the object is a "black hole." doesn't make any sense. The escape energy depends on the location you started from. E.g. if you start from the surface of the earth you need more energy to escape its gravitational field than if you start from a satellite's orbit. The horizon is the location at which a photon would need infinite energy to leave. Thus, it can't leave, no matter how large it's energy. Photons that start not at the horizon, but somewhat away from it can escape but while doing so they loose a significant amount of energy, i.e. their frequency gets redshifted.

The strings move in a five-dimensional curved space-time with a boundary. The boundary corresponds to the usual four dimensions, and the fifth dimension describes the motion away from this boundary into the interior of the curved space-time. In this five-dimensional space-time, there is a strong gravitational field pulling objects away from the boundary, and as a result time flows more slowly far away from the boundary than close to it. This also implies that an object that has a fixed proper size in the interior can appear to have a different size when viewed from the boundary (Fig. 1). Strings existing in the five-dimensional space-time can even look point-like when they are close to the boundary. Polchinski and Strassler1 show that when an energetic four-dimensional particle (such as an electron) is scattered from these strings (describing protons), the main contribution comes from a string that is close to the boundary and it is therefore seen as a point-like object. So a string-like interpretation of a proton is not at odds with the observation that there are point-like objects inside it.

"Colour full" discriptions of the particles? Oui! Non?

Superstring theory rules in the 5-D spacetime, but a so-called conformal field theory of point particles operates on the 4-D hologram. A black hole in the 5-D spacetime is equivalent to hot radiation on the hologram--for example, the hole and the radiation have the same entropy even though the physical origin of the entropy is completely different for each case. Although these two descriptions of the universe seem utterly unalike, no experiment could distinguish between them, even in principle. See here